Time to Double or Triple an Investment The formula t = ln m n ln ( 1 + r n ) can be used to find the number of years t required to multiply an investment m times when r is the per annum interest rate compounded n times a year. (a) How many years will it take to double the value of an IRA that compounds annually at the rate of 6 % ? (b) How many years will it take to triple the value of a savings account that compounds quarterly at an annual rate of 5 % ? (c) Give a derivation of this formula.
Time to Double or Triple an Investment The formula t = ln m n ln ( 1 + r n ) can be used to find the number of years t required to multiply an investment m times when r is the per annum interest rate compounded n times a year. (a) How many years will it take to double the value of an IRA that compounds annually at the rate of 6 % ? (b) How many years will it take to triple the value of a savings account that compounds quarterly at an annual rate of 5 % ? (c) Give a derivation of this formula.
Time to Double or Triple an Investment
The formula
can be used to find the number of years
required to multiply an investment
times when
is the per annum interest rate compounded
times a year.
(a) How many years will it take to double the value of an IRA that compounds annually at the rate of
?
(b) How many years will it take to triple the value of a savings account that compounds quarterly at an annual rate of
?
(c) Give a derivation of this formula.
Expert Solution
To determine
To find: The formula can be used to find the number of years required to multiply an investment times when is the per annum interest rate compounded times a year.
a. How many years will it take to double the value of an IRA that compounds annually at the rate of ?
Answer to Problem 67AYU
Solution:
a.
years
Explanation of Solution
Given:
The formula can be used to find the number of years required to multiply an investment times when is the per annum interest rate compounded times a year.
Calculation:
a. How many years will it take to double the value of an IRA that compounds annually at the rate of ?
Years
Expert Solution
To determine
To find: The formula can be used to find the number of years required to multiply an investment times when is the per annum interest rate compounded times a year.
b. How many years will it take to triple the value of a savings account that compounds quarterly at an annual rate of ?
Answer to Problem 67AYU
Solution:
b. years
Explanation of Solution
Given:
The formula can be used to find the number of years required to multiply an investment times when is the per annum interest rate compounded times a year.
Calculation:
b. How many years will it take to triple the value of a savings account that compounds quarterly at an annual rate of ?
years
Expert Solution
To determine
To find: The formula can be used to find the number of years required to multiply an investment times when is the per annum interest rate compounded times a year.
c. Give a derivation of this formula.
Answer to Problem 67AYU
Solution:
c. We know that
Amount becomes times
Taking ln on both sides we get
Explanation of Solution
Given:
The formula can be used to find the number of years required to multiply an investment times when is the per annum interest rate compounded times a year.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.